Potential of Mean Force of Hydrophobic Association: Dependence on Solute Size

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Influence of salt and temperature on the self-assembly of cyclic peptides in water: a molecular dynamics study

It is found in the literature that cyclic peptides (CPs) are able to self-assemble in water to form cyclic peptide nanotubes (CPNTs) and are used extensively in the field of nanotechnology. Several factors influence the formation and stability of these nanotubes in water. However, an extensive study of the contribution of several important factors is still lacking. The purpose of this study is to explore the effect of temperature and salt (NaCl) on the association tendency of CPs. Furthermore, the self-association behavior of CPs in aqueous solutions at various temperatures is also thoroughly discussed. Cyclo-[(Asp-D-Leu-Lys-D-Leu)₂] is considered for this study and a series of classical molecular dynamics (MD) simulations at three different temperatures, viz. 280 K, 300 K, and 320 K, both in pure water and in NaCl solutions of different concentrations are carried out. The calculations of radial distribution functions, preferential interaction parameters, cluster formation and hydrogen bonding properties suggest a strong influence of NaCl concentration on the association propensity of CPs. Low NaCl concentration hinders CP association while high NaCl concentration facilitates the association of CPs. Besides this, the association of CPs is found to be enhanced at low temperature. Furthermore, the thermodynamics of CP association is predominantly found to be enthalpy driven in both the presence and absence of salt. No crossover between enthalpy and entropy in CP association is observed. In addition, the MM-GBSA method is used to investigate the binding free energies of the CP rings that self-assembled to form nanotube like structures at all three temperatures.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

Influence of Temperature and Salt Concentration on the Hydrophobic Interactions of Adamantane and Hexane

One of the definitions of hydrophobic interactions is the aggregation of nonpolar particles in a polar solvent, such as water. While this phenomenon appears to be very simple, it is crucial for many complex processes, such as protein folding, to take place. In this work, the hydrophobic association of adamantane and hexane at various temperatures and ionic strengths was studied using molecular dynamics simulations with the AMBER 16.0 program and the GAFF force field. The potentials of mean force of hydrophobic dimer formation, as well as the excess free energy, excess energy, excess entropy, and excess heat capacity corresponding to the formation of the contact minimum, were determined and analyzed. For both systems, the depth of the contact minimum in the potential of mean force was found to increase with both temperature and ionic strength. The excess heat capacity of the association at the contact minimum and T = 298 K was found to be negative and to decrease, while the excess entropy and energy were found to be positive and to increase for both systems, the changes being more pronounced for the hexane dimer. The excess heat capacity is also greater in absolute value for the hexane dimer.

Influence of Ionic Strength on Hydrophobic Interactions in Water: Dependence on Solute Size and Shape

Hydrophobicity is a phenomenon of great importance in biology, chemistry, and biochemistry. It is defined as the interaction between nonpolar molecules or groups in water and their low solubility. Hydrophobic interactions affect many processes in water, for example, complexation, surfactant aggregation, and coagulation. These interactions play a pivotal role in the formation and stability of proteins or biological membranes. In the present study, we assessed the effect of ionic strength, solute size, and shape on hydrophobic interactions between pairs of nonpolar particles. Pairs of methane, neopentane, adamantane, fullerene, ethane, propane, butane, hexane, octane, and decane were simulated by molecular dynamics in AMBER 16.0 force field. As a solvent, TIP3P and TIP4PEW water models were used. Potential of mean force (PMF) plots of these dimers were determined at four values of ionic strength, 0, 0.04, 0.08, and 0.40 mol/dm³, to observe its impact on hydrophobic interactions. The characteristic shape of PMFs with three extrema (contact minimum, solvent-separated minimum, and desolvation maximum) was observed for most of the compounds for hydrophobic interactions. Ionic strength affected hydrophobic interactions. We observed a tendency to deepen contact minima with an increase in ionic strength value in the case of spherical and spheroidal molecules. Additionally, two-dimensional distribution functions describing water density and average number of hydrogen bonds between water molecules were calculated in both water models for adamantane and hexane. It was observed that the density of water did not significantly change with the increase in ionic strength, but the average number of hydrogen bonds changed. The latter tendency strongly depends on the water model used for simulations.

Hydrophobic hydration and pairwise hydrophobic interaction of Lennard-Jones and Mie particles in different water models

The study provides a deep computational analysis of the thermodynamic and structural features associated with the hydration of xenon, Xe, and its pairwise hydrophobic interaction (i.e., the potential of mean force, PMF), over a large temperature range. Xe is described both as a Lennard-Jones particle, LJ-Xe, and as a Mie particle, Mie-Xe (pseudo hard sphere). Three different water models are used: TIP3P-Ew, SPCE and TIP4P-2005. Mie-Xe is more hydrophobic than LJ-Xe due to the lack of the attractive energetic interactions with water molecules; its hydration, around room temperature, is opposed by a large and negative entropy change and a positive enthalpy change. The PMF of Mie-Xe is characterized by a deep minimum at contact distance whose depth increases with temperature, and whose magnitude is significantly larger than that obtained for LJ-Xe. The contact minimum configuration of Mie-Xe is favoured by a large positive entropy change and contrasted by a positive enthalpy change. These results are qualitatively the same regardless of the water model used. There is no clear connection between the values determined for the thermodynamic functions and the structural features of the hydration shells surrounding the single Mie-Xe and the couple of Mie-Xe particles in the contact minimum configuration. This confirms that the structural reorganization of water associated with such processes is characterized by an almost complete enthalpy-entropy compensation.

Physical origin underlying the prenucleation-cluster-mediated nonclassical nucleation pathways for calcium phosphate

The involvement of prenucleation clusters (PNCs) in crystallization from a supersaturated solution has been recently admitted within the framework of nonclassical nucleation theory; however, little is known about PNCs, at the quantitative level, for their formation mechanism and stability, the new phase formed by them, as well as their impact on nucleation barriers. Herein, using the sophisticated free energy calculations with a cumulative simulation time of over 5 μs, we identify a thermodynamically favored pathway of the PNC-mediated nucleation for calcium phosphate, starting with the ion pair association in solution. We demonstrate that such an ion association occurs not only between cations and anions, but also for the polyatomic species with charges of the same sign, which, in fact, leads to PNC formation via the consecutive coordination of the phosphate ions to calcium. The free energy decomposition calculations illustrate that the water phase is capable to either hinder or promote ion association for the abovementioned processes, and its specific role is intricately related to the characteristics of the hydration shell around calcium ions. The favorable interactions between the highly charged species play a crucial role in stabilizing the PNC complexes and the aggregates formed by PNCs. Furthermore, our present work reveals that the uptake of an extra calcium ion is the first and mandatory step to trigger PNC aggregation into amorphous calcium phosphate (ACP) by eliminating the related free energy barriers. Our theoretical study successfully provides quantitative explanations to a large set of experimental data in the field, which is currently under intense discussions associated with the nonclassical nucleation mechanism. The combination of computational methods developed in our present work offers a feasible and general solution to quantitatively and systematically study ion associations and crystal nucleation/growth in an aqueous solution at the atomic level, which are normally inaccessible to most of the existing experimental acquisitions.

Quantitatively Identifying the Roles of Interfacial Water and Solid Surface in Governing Peptide Adsorption

Understanding the molecular mechanism of protein adsorption on solids is critical to their applications in materials synthesis and tissue engineering. Although the water phase at the surface/water interface has been recognized as three types: bulk water, intermediate water phase and surface-bound water layers, the roles of the water and surface in determining the protein adsorption are not clearly identified, particularly at the quantitative level. Herein, we provide a methodology involving the combination of microsecond strengthen sampling simulation and force integration to quantitatively characterize the water-induced contribution and the peptide-surface interactions into the adsorption free energy. Using hydroxyapatite and graphene surfaces as examples, we demonstrate how the distinct interfacial features dominate the delicate force balance between these two thermodynamics parameters, leading to surface preference/resistance to peptide adsorption. Specifically, the water layer provides sustained repelling force against peptide adsorption, as indicated by a monotonic increase in the water-induced free energy profile, whereas the contribution from the surface-peptide interactions is thermodynamically favorable to peptide adsorptions. More importantly, the revealed adsorption mechanism is critically dictated by the distribution of water phase, which plays a crucial role in establishing the force balance between the interactions of the peptide with the water layer and the surface. For the HAP surface, the charged peptide exhibits strong binding affinity to the surface, due to the controlling contribution of peptide-surface interaction in the intermediate water phase. The surface-bound water layers are observed as the origin of bioresistance of solid surfaces toward the adsorption of charge-neutral peptides. The preferred peptide adsorption on the graphene, however, is dominated by the surface-induced component at the water layers adjacent to the surface. Our results further elucidate that the intermediate water phase significantly shortens the effective range of the surface dispersion force, in contrast to the observation on the hydrophilic surface.

Antifreeze Glycoproteins Bind Reversibly to Ice via Hydrophobic Groups

Antifreeze molecules allow organisms to survive in subzero environments. Antifreeze glycoproteins (AFGPs), produced by polar fish, are the most potent inhibitors of ice recrystallization. To date, the molecular mechanism by which AFGPs bind to ice has not yet been elucidated. Mutation experiments cannot resolve whether the binding occurs through the peptide, the saccharides, or both. Here, we use molecular simulations to determine the mechanism and driving forces for binding of AFGP8 to ice, its selectivity for the primary prismatic plane, and the molecular origin of its exceptional ice recrystallization activity. Consistent with experiments, AFGP8 in simulations preferentially adopts the PPII helix secondary structure in solution. We show that the segregation of hydrophilic and hydrophobic groups in the PPII helix is vital for ice binding. Binding occurs through adsorption of methyl groups of the peptide and disaccharides to ice, driven by the entropy of dehydration of the hydrophobic groups as they nest in the cavities at the ice surface. The selectivity to the primary prismatic plane originates in the deeper cavities it has compared to the basal plane. We estimate the free energy of binding of AFGP8 and the longer AFGPs4-6, and find them to be consistent with the reversible binding demonstrated in experiments. The simulations reveal that AFGP8 binds to ice through a myriad of conformations that it uses to diffuse through the ice surface and find ice steps, to which it strongly adsorbs. We interpret that the existence of multiple, weak binding sites is the key for the exceptional ice recrystallization inhibition activity of AFGPs.

Can Simple Interaction Models Explain Sequence-Dependent Effects in Peptide Homodimerization?

The development of rapid methods to explain and predict peptide interactions, aggregation, and self-assembly has become important to understanding amyloid disease pathology, the shelf stability of peptide therapeutics, and the design of novel peptide materials. Although experimental aggregation databases have been used to develop correlative and statistical models, molecular simulations offer atomic-level details that potentially provide greater physical insight and allow one to single out the most explanatory simple models. Here, we outline one such approach using a case study that develops homodimerization models for serine-glycine peptides with various hydrophobic leucine mutations. Using detailed all-atom simulations, we calculate reference dimerization free energy profiles and binding constants for a small peptide library. We then use statistical methods to systematically assess whether simple interaction models, which do not require expensive simulations and free energy calculation, can capture them. Surprisingly, some combinations of a few simple scaling laws well recapitulate the detailed, all-atom results with high accuracy. Specifically, we find that a recently proposed phenomenological hydrophobic force law and coarse measures of entropic effects in binding offer particularly high explanatory power, underscoring the physical relevance to association that these driving forces can play.

Simulation of self-assembly of polyzwitterions into vesicles

Using the Langevin dynamics method and a coarse-grained model, we have studied the formation of vesicles by hydrophobic polymers consisting of periodically placed zwitterion side groups in dilute salt-free aqueous solutions. The zwitterions, being permanent charge dipoles, provide long-range electrostatic correlations which are interfered by the conformational entropy of the polymer. Our simulations are geared towards gaining conceptual understanding in these correlated dipolar systems, where theoretical calculations are at present formidable. A competition between hydrophobic interactions and dipole-dipole interactions leads to a series of self-assembled structures. As the spacing d between the successive zwitterion side groups decreases, single chains undergo globule → disk → worm-like structures. We have calculated the Flory-Huggins χ parameter for these systems in terms of d and monitored the radius of gyration, hydrodynamic radius, spatial correlations among hydrophobic and dipole monomers, and dipole-dipole orientational correlation functions. During the subsequent stages of self-assembly, these structures lead to larger globules and vesicles as d is decreased up to a threshold value, below which no large scale morphology forms. The vesicles form via a polynucleation mechanism whereby disk-like structures form first, followed by their subsequent merger.

Shedding light on the hydrophobicity puzzle

A general theory of hydrophobic hydration and pairwise hydrophobic interaction has been developed in the last years. The main ingredient is the recognition that: (a) cavity creation (necessary to insert a solute molecule into water) causes a solvent-excluded volume effect that leads to a loss in the translational entropy of water molecules; (b) the merging of two cavities (necessary to form the contact minimum configuration of two nonpolar molecules) causes a decrease in the solvent-excluded volume effect and so an increase in the translational entropy of water molecules. The performance of the theoretical approach is tested by reproducing both the hydration thermodynamics of xenon and the thermodynamics associated with the formation of the contact minimum configuration of two xenon atoms, over a large temperature range.

Cononsolvency behavior of hydrophobes in water + methanol mixtures

The molecular origin of cononsolvency behavior is explored using molecular dynamics simulations.

A continuum solvent model of ion-ion interactions in water

The calculation of ion-ion interactions in water is a problem of long standing importance. Modelling these interactions is a prerequisite to explaining Hofmeister (specific ion) effects. We here generalize our solvation model of ions to calculate the free energy of two ions in water as a function of separation. The same procedure has previously been applied to calculate ion interactions with the air-water interface successfully. The Conductor like Screening Model (COSMO) is used. This treats the ions on a quantum mechanical level and calculates numerically the electrostatic response of the surrounding solvent. Estimates of the change in the cavity formation energy and the change in the ion-water dispersion energy as the ions approach are included separately. The calculated interaction potentials are too attractive and this is a significant issue. However, they do reproduce the affinity of similarly sized ions for each other, which is a crucial property of these potentials. They are also oscillatory, another important property. We normalize the potentials to reduce the over-attraction, and good correlation with experimental values is achieved. We identify the driving contributions to this like-prefers-like behaviour. We then put forward a plausible hypothesis for the over-attraction of the potentials. An agreeable feature of our approach is that it does not rely on salt specific parameters deliberately adjusted to reproduce experimental values.

Simulation optimization of spherical non-polar guest recognition by deep-cavity cavitands

Biomimetic deep-cavity cavitand hosts possess unique recognition and encapsulation properties that make them capable of selectively binding a range of non-polar guests within their hydrophobic pocket. Adamantane based derivatives which snuggly fit within the pocket of octa-acid deep cavity cavitands exhibit some of the strongest host binding. Here we explore the roles of guest size and attractiveness on optimizing guest binding to form 1:1 complexes with octa-acid cavitands in water. Specifically we simulate the water-mediated interactions of the cavitand with adamantane and a range of simple Lennard-Jones guests of varying diameter and attractive well-depth. Initial simulations performed with methane indicate hydrated methanes preferentially reside within the host pocket, although these guests frequently trade places with water and other methanes in bulk solution. The interaction strength of hydrophobic guests increases with increasing size from sizes slightly smaller than methane to Lennard-Jones guests comparable in size to adamantane. Over this guest size range the preferential guest binding location migrates from the bottom of the host pocket upwards. For guests larger than adamantane, however, binding becomes less favorable as the minimum in the potential-of-mean force shifts to the cavitand face around the portal. For a fixed guest diameter, the Lennard-Jones well-depth is found to systematically shift the guest-host potential-of-mean force to lower free energies, however, the optimal guest size is found to be insensitive to increasing well-depth. Ultimately our simulations show that adamantane lies within the optimal range of guest sizes with significant attractive interactions to match the most tightly bound Lennard-Jones guests studied.

A nucleation-based method to study hydrophobic interactions under confinement: enhanced hydrophobic association driven by energetic contributions

A novel simulation approach was developed and applied to the study of hydrophobic interactions for a small hydrophobic solute pair under confinement. In this method, the aggregation-volume-bias Monte Carlo algorithm, developed originally for nucleation studies, is used to evaluate the association free energy with water molecules for a methane pair through the gradual addition of water molecules into a nanometer-sized sphere. Through a thermodynamic cycle, this method allows for a convenient examination of the free energy difference between two different solvated configurations without sampling any of the configurations in between. The potential of mean force (PMF) for a methane pair under confinement obtained from this method reveals that the stability of the contact pair configuration can be enhanced compared to that in bulk water, which is in agreement with previous studies. Also, constraining the center of this methane pair at the center of this confined volume yields a PMF with a metastable solvent separated configuration, resembling more closely the PMF from the bulk-phase system compared to previous studies in which this solvent-separated minimum was found to be completely absent. A combination with histogram reweighting enables the study of this association behavior at different thermodynamic conditions without additional simulations. From a comprehensive thermodynamic analysis, it is evident that such hydrophobic association, known to be entropically driven in the bulk-phase system at ambient conditions, is entropically favorable only when a suitable range of solvent molecules is added to the confined system. More importantly, the energetic contributions are a favorable factor that explains the enhanced hydrophobic association toward the high number of solvent molecules.

The application of the integral equation theory to study the hydrophobic interaction

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy.

A Density Functional Theory Evaluation of Hydrophobic Solvation: Ne, Ar and Kr in a 50-Water Cluster. Implications for the Hydrophobic Effect

The physical explanation for the hydrophobic effect has been the subject of disagreement. Physical organic chemists tend to use a explanation related to pressure, while many biochemists prefer an explanation that involves decreased entropy of the aqueous solvent. We present DFT calculations at the B3LYP/6-31G(d,p) and X3LYP/6-31G(d,p) levels on the solvation of three noble gases (Ne, Ar, and Kr) in clusters of 50 waters. Vibrational analyses show no substantial decreases in the vibrational entropies of the waters in any of the three clusters. The observed positive free energies of transfer from the gas phase or from nonpolar solvents to water appear to be due to the work needed to make a suitable hole in the aqueous solvent. We distinguish between hydrophobic solvations (explicitly studied here) and the hydrophobic effect that occurs when a solute (or transition state) can decrease its volume through conformational change (which is not possible for the noble gases).

Communication: Direct observation of a hydrophobic bond in loop closure of a capped (-OCH2CH2-)n oligomer in water

The small r variation of the probability density P(r) for end-to-end separations of a -CH(2)CH(3) capped (-OCH(2)CH(2)-)(n) oligomer in water is computed to be closely similar to the CH(4)···CH(4) potential of mean force under the same circumstances. Since the aqueous solution CH(4)···CH(4) potential of mean force is the natural physical definition of a primitive hydrophobic bond, the present result identifies an experimentally accessible circumstance for direct observation of a hydrophobic bond which has not been observed previously because of the low solubility of CH(4) in water. The physical picture is that the soluble chain molecules carry the capping groups into aqueous solution, and permits them to find one another with reasonable frequency. Comparison with the corresponding results without the solvent shows that hydration of the solute oxygen atoms swells the chain molecule globule. This supports the view that the chain molecule globule might have a secondary effect on the hydrophobic interaction that is of first interest here. The volume of the chain molecule globule is important for comparing the probabilities with and without solvent because it characterizes the local concentration of capping groups. Study of other capping groups to enable x-ray and neutron diffraction measurements of P(r) is discussed.

Direct Measurement of the Kinetics and Thermodynamics of Association of Hydrophobic Molecules from Molecular Dynamics Simulations

A detailed study of the kinetics and thermodynamics of associations of model hydrophobic molecules is likely to be valuable for understanding the fundamental driving forces for processes such as protein folding and protein-protein association. To this end, we present results from a series of 500 ns long molecular dynamics (MD) simulations examining associations of 13 types of different alkane pairs in explicit water. In addition to providing accurate measurements of the association thermodynamics, the unbiased nature of the configurational sampling in the MD simulations allows the association and dissociation kinetics to be directly quantified. We show that by choosing a suitable reaction coordinate, the computed free energies of all of the alkane-alkane complexes can be linearly related to their buried molecular surface areas, that their dissociation kinetics can be reliably estimated from the height of the barrier on the computed free energy surfaces, and that their association kinetics are effectively diffusion-limited.

Advances in implicit models of water solvent to compute conformational free energy and molecular dynamics of proteins at constant pH

Modern implicit solvent models for macromolecular simulations in water-proton bath are considered. The fundamental quantity that implicit models approximate is the solute potential of mean force, which is obtained by averaging over solvent degrees of freedom. The implicit solvent models suggest practical ways to calculate free energies of macromolecular conformations taking into account equilibrium interactions with water solvent and proton bath, while the explicit solvent approach is unable to do that due to the need to account for a large number of solvent degrees of freedom. The most advanced realizations of the implicit continuum models by different research groups are discussed, their accuracy are examined, and some applications of the implicit solvent models to macromolecular modeling, such as free energy calculations, protein folding, and constant pH molecular dynamics are highlighted.

Probing solvation decay length in order to characterize hydrophobicity-induced bead-bead attractive interactions in polymer chains

In this paper, we quantitatively demonstrate that exponentially decaying attractive potentials can effectively mimic strong hydrophobic interactions between monomer units of a polymer chain dissolved in aqueous solvent. Classical approaches to modeling hydrophobic solvation interactions are based on invariant attractive length scales. However, we demonstrate here that the solvation interaction decay length may need to be posed as a function of the relative separation distances and the sizes of the interacting species (or beads or monomers) to replicate the necessary physical interactions. As an illustrative example, we derive a universal scaling relationship for a given solute-solvent combination between the solvation decay length, the bead radius, and the distance between the interacting beads. With our formalism, the hydrophobic component of the net attractive interaction between monomer units can be synergistically accounted for within the unified framework of a simple exponentially decaying potential law, where the characteristic decay length incorporates the distinctive and critical physical features of the underlying interaction. The present formalism, even in a mesoscopic computational framework, is capable of incorporating the essential physics of the appropriate solute-size dependence and solvent-interaction dependence in the hydrophobic force estimation, without explicitly resolving the underlying molecular level details.

Potential of mean force of association of large hydrophobic particles: toward the nanoscale limit

The potentials of mean force (PMFs) were determined, in both water with the TIP3P water model and in vacuo, for systems involving formation of nonpolar dimers composed of bicyclooctane, adamantane (both an all-atom model and a sphere with the radius of 3.4 A representing adamantane), and fullerene, respectively. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field were carried out for each pair under both environmental conditions. The PMFs were calculated by using the weighted histogram analysis method. The results were compared with our previously determined PMF for neopentane. The shape of the PMFs for dimers of all four nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule; for larger molecules they shift toward larger distances. Comparison of the PMFs of the bicyclooctane, adamantane, and fullerene dimers in water and in vacuo shows that hydrophobic interactions in each dimer are different from that for the dimer of neopentane. Interactions in the bicyclooctane, adamantane, and fullerene dimers are stronger in vacuo than in water. These dimers cannot be treated as classical, spherical, hydrophobic objects. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from that in explicit solvent. The solvent contribution to the PMFs of bicyclooctane, adamantane, and fullerene is positive, as opposed to that of neopentane. The water molecules in the first solvation sphere of both adamantane and neopentane dimers are more ordered as compared to bulk water, with their dipole moments pointing away from the surface of the dimers. The average number of hydrogen bonds per water molecule in the first hydration shell of adamantane is smaller compared to that in bulk water, but this shell is thicker for all-atom adamantane than for neopentane or a spherical model of adamantane. In the second hydration shell, the average number of hydrogen bonds is greater compared to that in bulk water only for neopentane and a spherical model of adamantane but not for the all-atom model. The strength of the hydrophobic interactions shows a linear dependence on the number of carbon atoms both in water and in vacuo. Smaller nonpolar particles interact more strongly in water than in vacuo. For larger molecules, such as bicyclooctane, adamantane and fullerene, the reversed tendency is observed.

Dimerization thermodynamics of large hydrophobic plates: a scaled particle theory study

The temperature dependence of the association thermodynamics of two large hydrophobic plates has been determined by means of molecular dynamics simulations ( Zangi , R. ; Berne , B. J. J. Phys. Chem. B 2008 , 112 , 8634 - 8644 ). This offers the opportunity to test the ability of an approach grounded on the basic concept that the reduction in the solvent-excluded volume plays a fundamental role and on a suitable application of scaled particle theory to reproduce such association thermodynamic functions over an extended temperature range. The results indicate that the Gibbs energy change is always largely negative and little dependent on temperature. The enthalpy change is positive at 0 degrees C, small negative at 25 degrees C, and largely negative at 100 degrees C. The entropy change is largely positive at 0 degrees C, passes through zero at about 85 degrees C, and is negative at 100 degrees C. The strong temperature dependence of the enthalpy and entropy changes, due to a large negative heat capacity change, is almost exactly compensating, so that the Gibbs energy change is little affected. The most part of the present results proves to be in more than qualitative agreement with those obtained by means of molecular dynamics simulations.

Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.